Coverage report

(************************************************************************)
(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017     *)
(*   \VV/  **************************************************************)
(*    //   *      This file is distributed under the terms of the       *)
(*         *       GNU Lesser General Public License Version 2.1        *)
(************************************************************************)

(*i*)
open Pp
open CErrors
open Util
open Names
open Nameops
open Constr
open Termops
open Libnames
open Globnames
open Impargs
open CAst
open Constrexpr
open Constrexpr_ops
open Notation_ops
open Glob_term
open Glob_ops
open Pattern
open Nametab
open Notation
open Detyping
open Misctypes
open Decl_kinds

module NamedDecl = Context.Named.Declaration
(*i*)

(* Translation from glob_constr to front constr *)

(**********************************************************************)
(* Parametrization                                                    *)

(* This governs printing of local context of references *)
let print_arguments = ref false

(* If true, prints local context of evars *)
let print_evar_arguments = Detyping.print_evar_arguments

(* This governs printing of implicit arguments.  When
   [print_implicits] is on then [print_implicits_explicit_args] tells
   how implicit args are printed. If on, implicit args are printed
   with the form (id:=arg) otherwise arguments are printed normally and
   the function is prefixed by "@" *)
let print_implicits = ref false
let print_implicits_explicit_args = ref false

(* Tells if implicit arguments not known to be inferable from a rigid
   position are systematically printed *)
let print_implicits_defensive = ref true

(* This forces printing of coercions *)
let print_coercions = ref false

(* This forces printing universe names of Type{.} *)
let print_universes = Detyping.print_universes

(* This suppresses printing of primitive tokens (e.g. numeral) and notations *)
let print_no_symbol = ref false

(**********************************************************************)
(* Turning notations and scopes on and off for printing *)
module IRuleSet = Set.Make(struct
    type t = interp_rule
    let compare x y = Pervasives.compare x y
  end)

let inactive_notations_table =
  Summary.ref ~name:"inactive_notations_table" (IRuleSet.empty)
let inactive_scopes_table    =
  Summary.ref ~name:"inactive_scopes_table" CString.Set.empty

let show_scope scopt =
  match scopt with
  | None -> str ""
  | Some sc -> spc () ++ str "in scope" ++ spc () ++ str sc

let _show_inactive_notations () =
  begin
    if CString.Set.is_empty !inactive_scopes_table
    then
      Feedback.msg_notice (str "No inactive notation scopes.")
    else
      let _ = Feedback.msg_notice (str "Inactive notation scopes:") in
      CString.Set.iter (fun sc -> Feedback.msg_notice (str "  " ++ str sc))
        !inactive_scopes_table
  end;
  if IRuleSet.is_empty !inactive_notations_table
  then
    Feedback.msg_notice (str "No individual inactive notations.")
  else
    let _ = Feedback.msg_notice (str "Inactive notations:") in
    IRuleSet.iter
      (function
       | NotationRule (scopt, ntn) ->
         Feedback.msg_notice (str ntn ++ show_scope scopt)
       | SynDefRule kn -> Feedback.msg_notice (str (Names.KerName.to_string kn)))
      !inactive_notations_table

let deactivate_notation nr =
  match nr with
  | SynDefRule kn ->
     (* shouldn't we check wether it is well defined? *)
     inactive_notations_table := IRuleSet.add nr !inactive_notations_table
  | NotationRule (scopt, ntn) ->
     match availability_of_notation (scopt, ntn) (scopt, []) with
     | None -> user_err ~hdr:"Notation"
                        (str ntn ++ spc () ++ str "does not exist"
                         ++ (match scopt with
                             | None -> spc () ++ str "in the empty scope."
                             | Some _ -> show_scope scopt ++ str "."))
     | Some _ ->
        if IRuleSet.mem nr !inactive_notations_table then
          Feedback.msg_warning
            (str "Notation" ++ spc () ++ str ntn ++ spc ()
             ++ str "is already inactive" ++ show_scope scopt ++ str ".")
        else inactive_notations_table := IRuleSet.add nr !inactive_notations_table

let reactivate_notation nr =
  try
    inactive_notations_table :=
      IRuleSet.remove nr !inactive_notations_table
  with Not_found ->
    match nr with
    | NotationRule (scopt, ntn) ->
       Feedback.msg_warning (str "Notation" ++ spc () ++ str ntn ++ spc ()
                             ++ str "is already active" ++ show_scope scopt ++
  str ".")
    | SynDefRule kn ->
       Feedback.msg_warning
         (str "Notation" ++ spc () ++ str (Names.KerName.to_string kn)
          ++ spc () ++ str "is already active.")


let deactivate_scope sc =
  ignore (find_scope sc); (* ensures that the scope exists *)
  if CString.Set.mem sc !inactive_scopes_table
  then
    Feedback.msg_warning (str "Notation Scope" ++ spc () ++ str sc ++ spc ()
                          ++ str "is already inactive.")
  else
    inactive_scopes_table := CString.Set.add sc !inactive_scopes_table

let reactivate_scope sc =
  try
    inactive_scopes_table := CString.Set.remove sc !inactive_scopes_table
  with Not_found ->
    Feedback.msg_warning (str "Notation Scope" ++ spc () ++ str sc ++ spc ()
                          ++ str "is already active.")

let is_inactive_rule nr =
  IRuleSet.mem nr !inactive_notations_table ||
  match nr with
    | NotationRule (Some sc, ntn) -> CString.Set.mem sc !inactive_scopes_table
    | NotationRule (None, ntn) -> false
    | SynDefRule _ -> false

(* args: notation, scope, activate/deactivate *)
let toggle_scope_printing ~scope ~activate =
  if activate then
    reactivate_scope scope
  else
    deactivate_scope scope

let toggle_notation_printing ?scope ~notation ~activate =
  if activate then
    reactivate_notation (NotationRule (scope, notation))
  else
    deactivate_notation (NotationRule (scope, notation))

(* This governs printing of projections using the dot notation symbols *)
let print_projections = ref false

let print_meta_as_hole = ref false

let with_universes f = Flags.with_option print_universes f
let with_meta_as_hole f = Flags.with_option print_meta_as_hole f
let without_symbols f = Flags.with_option print_no_symbol f

let without_specific_symbols l =
  Flags.with_modified_ref inactive_notations_table
    (fun tbl -> IRuleSet.(union (of_list l) tbl))

(**********************************************************************)
(* Control printing of records *)

(* Set Record Printing flag *)
let record_print = ref true

let _ =
  let open Goptions in
  declare_bool_option
    { optdepr  = false;
      optname  = "record printing";
      optkey   = ["Printing";"Records"];
      optread  = (fun () -> !record_print);
      optwrite = (fun b -> record_print := b) }


let is_record indsp =
  try
    let _ = Recordops.lookup_structure indsp in
    true
  with Not_found -> false

let encode_record r =
  let indsp = global_inductive r in
  if not (is_record indsp) then
    user_err ?loc:(loc_of_reference r) ~hdr:"encode_record"
      (str "This type is not a structure type.");
  indsp

module PrintingRecordRecord =
  PrintingInductiveMake (struct
    let encode = encode_record
    let field = "Record"
    let title = "Types leading to pretty-printing using record notation: "
    let member_message s b =
      str "Terms of " ++ s ++
      str
      (if b then " are printed using record notation"
      else " are not printed using record notation")
  end)

module PrintingRecordConstructor =
  PrintingInductiveMake (struct
    let encode = encode_record
    let field = "Constructor"
    let title = "Types leading to pretty-printing using constructor form: "
    let member_message s b =
      str "Terms of " ++ s ++
      str
      (if b then " are printed using constructor form"
      else " are not printed using constructor form")
  end)

module PrintingRecord = Goptions.MakeRefTable(PrintingRecordRecord)
module PrintingConstructor = Goptions.MakeRefTable(PrintingRecordConstructor)

(**********************************************************************)
(* Various externalisation functions *)

let insert_delimiters e = function
  | None -> e
  | Some sc -> CAst.make @@ CDelimiters (sc,e)

let insert_pat_delimiters ?loc p = function
  | None -> p
  | Some sc -> CAst.make ?loc @@ CPatDelimiters (sc,p)

let insert_pat_alias ?loc p = function
  | Anonymous -> p
  | Name id -> CAst.make ?loc @@ CPatAlias (p,id)

(**********************************************************************)
(* conversion of references                                           *)

let extern_evar n l = CEvar (n,l)

(** We allow customization of the global_reference printer.
    For instance, in the debugger the tables of global references
    may be inaccurate *)

let default_extern_reference ?loc vars r =
  Qualid (Loc.tag ?loc @@ shortest_qualid_of_global vars r)

let my_extern_reference = ref default_extern_reference

let set_extern_reference f = my_extern_reference := f
let get_extern_reference () = !my_extern_reference

let extern_reference ?loc vars l = !my_extern_reference ?loc vars l

(**********************************************************************)
(* mapping patterns to cases_pattern_expr                                *)

let add_patt_for_params ind l =
  if !Flags.in_debugger then l else
    Util.List.addn (Inductiveops.inductive_nparamdecls ind) (CAst.make @@ CPatAtom None) l

let add_cpatt_for_params ind l =
  if !Flags.in_debugger then l else
    Util.List.addn  (Inductiveops.inductive_nparamdecls ind) (DAst.make @@ PatVar Anonymous) l

let drop_implicits_in_patt cst nb_expl args =
  let impl_st = (implicits_of_global cst) in
  let impl_data = extract_impargs_data impl_st in
  let rec impls_fit l = function
    |[],t -> Some (List.rev_append l t)
    |_,[] -> None
    |h::t, { CAst.v = CPatAtom None }::tt when is_status_implicit h -> impls_fit l (t,tt)
    |h::_,_ when is_status_implicit h -> None
    |_::t,hh::tt -> impls_fit (hh::l) (t,tt)
  in let rec aux = function
    |[] -> None
    |(_,imps)::t -> match impls_fit [] (imps,args) with
        |None -> aux t
        |x -> x
     in
     if Int.equal nb_expl 0 then aux impl_data
     else
       let imps = List.skipn_at_least nb_expl (select_stronger_impargs impl_st) in
       impls_fit [] (imps,args)

let destPrim = function { CAst.v = CPrim t } -> Some t | _ -> None
let destPatPrim = function { CAst.v = CPatPrim t } -> Some t | _ -> None

let is_number s =
  let rec aux i =
    Int.equal (String.length s) i ||
    match s.[i] with '0'..'9' -> aux (i+1) | _ -> false
  in aux 0

let is_zero s =
  let rec aux i =
    Int.equal (String.length s) i || (s.[i] == '0' && aux (i+1))
  in aux 0

let make_notation_gen loc ntn mknot mkprim destprim l =
  match ntn,List.map destprim l with
    (* Special case to avoid writing "- 3" for e.g. (Z.opp 3) *)
    | "- _", [Some (Numeral (p,true))] when not (is_zero p) ->
        mknot (loc,ntn,([mknot (loc,"( _ )",l)]))
    | _ ->
        match decompose_notation_key ntn, l with
        | [Terminal "-"; Terminal x], [] when is_number x ->
           mkprim (loc, Numeral (x,false))
        | [Terminal x], [] when is_number x ->
           mkprim (loc, Numeral (x,true))
        | _ -> mknot (loc,ntn,l)

let make_notation loc ntn (terms,termlists,binders as subst) =
  if not (List.is_empty termlists) || not (List.is_empty binders) then
    CAst.make ?loc @@ CNotation (ntn,subst)
  else
    make_notation_gen loc ntn
      (fun (loc,ntn,l) -> CAst.make ?loc @@ CNotation (ntn,(l,[],[])))
      (fun (loc,p) -> CAst.make ?loc @@ CPrim p)
      destPrim terms

let make_pat_notation ?loc ntn (terms,termlists as subst) args =
  if not (List.is_empty termlists) then (CAst.make ?loc @@ CPatNotation (ntn,subst,args)) else
  make_notation_gen loc ntn
    (fun (loc,ntn,l) -> CAst.make ?loc @@ CPatNotation (ntn,(l,[]),args))
    (fun (loc,p)     -> CAst.make ?loc @@ CPatPrim p)
    destPatPrim terms

let mkPat ?loc qid l = CAst.make ?loc @@
  (* Normally irrelevant test with v8 syntax, but let's do it anyway *)
  if List.is_empty l then CPatAtom (Some qid) else CPatCstr (qid,None,l)

let pattern_printable_in_both_syntax (ind,_ as c) =
  let impl_st = extract_impargs_data (implicits_of_global (ConstructRef c)) in
  let nb_params = Inductiveops.inductive_nparams ind in
  List.exists (fun (_,impls) ->
    (List.length impls >= nb_params) &&
      let params,args = Util.List.chop nb_params impls in
      (List.for_all is_status_implicit params)&&(List.for_all (fun x -> not (is_status_implicit x)) args)
  ) impl_st

let lift f c =
  let loc = c.CAst.loc in
  CAst.make ?loc (f ?loc (DAst.get c))

 (* Better to use extern_glob_constr composed with injection/retraction ?? *)
let rec extern_cases_pattern_in_scope (scopes:local_scopes) vars pat =
  try
    if !Flags.in_debugger || !Flags.raw_print || !print_no_symbol then raise No_match;
    let (na,sc,p) = uninterp_prim_token_cases_pattern pat in
    match availability_of_prim_token p sc scopes with
      | None -> raise No_match
      | Some key ->
        let loc = cases_pattern_loc pat in
        insert_pat_alias ?loc (insert_pat_delimiters ?loc (CAst.make ?loc @@ CPatPrim p) key) na
  with No_match ->
    try
      if !Flags.in_debugger || !Flags.raw_print || !print_no_symbol then raise No_match;
      extern_notation_pattern scopes vars pat
        (uninterp_cases_pattern_notations pat)
    with No_match ->
      lift (fun ?loc -> function
        | PatVar (Name id) -> CPatAtom (Some (Ident (loc,id)))
        | PatVar (Anonymous) -> CPatAtom None
        | PatCstr(cstrsp,args,na) ->
          let args = List.map (extern_cases_pattern_in_scope scopes vars) args in
          let p =
            try
              if !Flags.raw_print then raise Exit;
              let projs = Recordops.lookup_projections (fst cstrsp) in
              let rec ip projs args acc =
                match projs, args with
                  | [], [] -> acc
                  | proj :: q, pat :: tail ->
                     let acc =
                       match proj, pat with
                       | _, { CAst.v = CPatAtom None } ->
                          (* we don't want to have 'x := _' in our patterns *)
                          acc
                       | Some c, _ ->
                          ((extern_reference ?loc Id.Set.empty (ConstRef c), pat) :: acc)
                       | _ -> raise No_match in
                     ip q tail acc
                  | _ -> assert false
              in
              CPatRecord(List.rev (ip projs args []))
            with
                Not_found | No_match | Exit ->
                  let c = extern_reference ?loc Id.Set.empty (ConstructRef cstrsp) in
                  if !asymmetric_patterns then
                    if pattern_printable_in_both_syntax cstrsp
                    then CPatCstr (c, None, args)
                    else CPatCstr (c, Some (add_patt_for_params (fst cstrsp) args), [])
                  else
                    let full_args = add_patt_for_params (fst cstrsp) args in
                    match drop_implicits_in_patt (ConstructRef cstrsp) 0 full_args with
                      | Some true_args -> CPatCstr (c, None, true_args)
                      | None           -> CPatCstr (c, Some full_args, [])
          in (insert_pat_alias ?loc (CAst.make ?loc p) na).v
        ) pat
and apply_notation_to_pattern ?loc gr ((subst,substlist),(nb_to_drop,more_args))
    (tmp_scope, scopes as allscopes) vars =
  function
    | NotationRule (sc,ntn) ->
      begin
        match availability_of_notation (sc,ntn) allscopes with
          (* Uninterpretation is not allowed in current context *)
          | None -> raise No_match
          (* Uninterpretation is allowed in current context *)
          | Some (scopt,key) ->
            let scopes' = Option.List.cons scopt scopes in
            let l =
              List.map (fun (c,(scopt,scl)) ->
                extern_cases_pattern_in_scope (scopt,scl@scopes') vars c)
                subst in
            let ll =
              List.map (fun (c,(scopt,scl)) ->
                let subscope = (scopt,scl@scopes') in
                List.map (extern_cases_pattern_in_scope subscope vars) c)
                substlist in
            let l2 = List.map (extern_cases_pattern_in_scope allscopes vars) more_args in
            let l2' = if !asymmetric_patterns || not (List.is_empty ll) then l2
              else
                match drop_implicits_in_patt gr nb_to_drop l2 with
                  |Some true_args -> true_args
                  |None -> raise No_match
            in
            insert_pat_delimiters ?loc
              (make_pat_notation ?loc ntn (l,ll) l2') key
      end
    | SynDefRule kn ->
      let qid = Qualid (Loc.tag ?loc @@ shortest_qualid_of_syndef vars kn) in
      let l1 =
        List.rev_map (fun (c,(scopt,scl)) ->
          extern_cases_pattern_in_scope (scopt,scl@scopes) vars c)
          subst in
      let l2 = List.map (extern_cases_pattern_in_scope allscopes vars) more_args in
      let l2' = if !asymmetric_patterns then l2
        else
          match drop_implicits_in_patt gr (nb_to_drop + List.length l1) l2 with
            |Some true_args -> true_args
            |None -> raise No_match
      in
      assert (List.is_empty substlist);
      mkPat ?loc qid (List.rev_append l1 l2')
and extern_notation_pattern (tmp_scope,scopes as allscopes) vars t = function
  | [] -> raise No_match
  | (keyrule,pat,n as _rule)::rules ->
    try
      if is_inactive_rule keyrule then raise No_match;
      let loc = t.loc in
      match DAst.get t with
        | PatCstr (cstr,_,na) ->
          let p = apply_notation_to_pattern ?loc (ConstructRef cstr)
            (match_notation_constr_cases_pattern t pat) allscopes vars keyrule in
          insert_pat_alias ?loc p na
        | PatVar Anonymous -> CAst.make ?loc @@ CPatAtom None
        | PatVar (Name id) -> CAst.make ?loc @@ CPatAtom (Some (Ident (loc,id)))
    with
        No_match -> extern_notation_pattern allscopes vars t rules

let rec extern_notation_ind_pattern allscopes vars ind args = function
  | [] -> raise No_match
  | (keyrule,pat,n as _rule)::rules ->
    try
      if is_inactive_rule keyrule then raise No_match;
      apply_notation_to_pattern (IndRef ind)
        (match_notation_constr_ind_pattern ind args pat) allscopes vars keyrule
    with
        No_match -> extern_notation_ind_pattern allscopes vars ind args rules

let extern_ind_pattern_in_scope (scopes:local_scopes) vars ind args =
  (* pboutill: There are letins in pat which is incompatible with notations and
     not explicit application. *)
  if !Flags.in_debugger||Inductiveops.inductive_has_local_defs ind then
    let c = extern_reference vars (IndRef ind) in
    let args = List.map (extern_cases_pattern_in_scope scopes vars) args in
    CAst.make @@ CPatCstr (c, Some (add_patt_for_params ind args), [])
  else
    try
      if !Flags.raw_print || !print_no_symbol then raise No_match;
      let (sc,p) = uninterp_prim_token_ind_pattern ind args in
      match availability_of_prim_token p sc scopes with
        | None -> raise No_match
        | Some key ->
          insert_pat_delimiters (CAst.make @@ CPatPrim p) key
    with No_match ->
      try
        if !Flags.raw_print || !print_no_symbol then raise No_match;
        extern_notation_ind_pattern scopes vars ind args
          (uninterp_ind_pattern_notations ind)
    with No_match ->
      let c = extern_reference vars (IndRef ind) in
      let args = List.map (extern_cases_pattern_in_scope scopes vars) args in
      match drop_implicits_in_patt (IndRef ind) 0 args with
           |Some true_args -> CAst.make @@ CPatCstr (c, None, true_args)
           |None           -> CAst.make @@ CPatCstr (c, Some args, [])

let extern_cases_pattern vars p =
  extern_cases_pattern_in_scope (None,[]) vars p

(**********************************************************************)
(* Externalising applications *)

let occur_name na aty =
  match na with
    | Name id -> occur_var_constr_expr id aty
    | Anonymous -> false

let is_projection nargs = function
  | Some r when not !Flags.in_debugger && not !Flags.raw_print && !print_projections ->
    (try
       let n = Recordops.find_projection_nparams r + 1 in
         if n <= nargs then Some n
         else None
     with Not_found -> None)
  | _ -> None

let is_hole = function CHole _ | CEvar _ -> true | _ -> false

let is_significant_implicit a =
  not (is_hole (a.CAst.v))

let is_needed_for_correct_partial_application tail imp =
  List.is_empty tail && not (maximal_insertion_of imp)

exception Expl

(* Implicit args indexes are in ascending order *)
(* inctx is useful only if there is a last argument to be deduced from ctxt *)
let explicitize inctx impl (cf,f) args =
  let impl = if !Constrintern.parsing_explicit then [] else impl in
  let n = List.length args in
  let rec exprec q = function
    | a::args, imp::impl when is_status_implicit imp ->
        let tail = exprec (q+1) (args,impl) in
        let visible =
          !Flags.raw_print ||
          (!print_implicits && !print_implicits_explicit_args) ||
          (is_needed_for_correct_partial_application tail imp) ||
          (!print_implicits_defensive &&
           (not (is_inferable_implicit inctx n imp) || !Flags.beautify) &&
           is_significant_implicit (Lazy.force a))
        in
        if visible then
          (Lazy.force a,Some (Loc.tag @@ ExplByName (name_of_implicit imp))) :: tail
        else
          tail
    | a::args, _::impl -> (Lazy.force a,None) :: exprec (q+1) (args,impl)
    | args, [] -> List.map (fun a -> (Lazy.force a,None)) args (*In case of polymorphism*)
    | [], (imp :: _) when is_status_implicit imp && maximal_insertion_of imp -> 
      (* The non-explicit application cannot be parsed back with the same type *)
      raise Expl
    | [], _ -> []
  in
  let ip = is_projection (List.length args) cf in
  let expl () = 
    match ip with
    | Some i ->
      if not (List.is_empty impl) && is_status_implicit (List.nth impl (i-1)) then
        raise Expl
      else
        let (args1,args2) = List.chop i args in
        let (impl1,impl2) = if List.is_empty impl then [],[] else List.chop i impl in
        let args1 = exprec 1 (args1,impl1) in
        let args2 = exprec (i+1) (args2,impl2) in
        let ip = Some (List.length args1) in
          CApp ((ip,f),args1@args2)
    | None ->
      let args = exprec 1 (args,impl) in
        if List.is_empty args then f.CAst.v else CApp ((None, f), args)
  in
    try expl ()
    with Expl -> 
      let f',us = match f with { CAst.v = CRef (f,us) } -> f,us | _ -> assert false in
      let ip = if !print_projections then ip else None in
        CAppExpl ((ip, f', us), List.map Lazy.force args)

let is_start_implicit = function
  | imp :: _ -> is_status_implicit imp && maximal_insertion_of imp
  | [] -> false

let extern_global impl f us =
  if not !Constrintern.parsing_explicit && is_start_implicit impl
  then
    CAppExpl ((None, f, us), [])
  else
    CRef (f,us)

let extern_app inctx impl (cf,f) us args =
  if List.is_empty args then
    (* If coming from a notation "Notation a := @b" *)
    CAppExpl ((None, f, us), [])
  else if not !Constrintern.parsing_explicit &&
    ((!Flags.raw_print ||
      (!print_implicits && not !print_implicits_explicit_args)) &&
     List.exists is_status_implicit impl)
  then
    let args = List.map Lazy.force args in
    CAppExpl ((is_projection (List.length args) cf,f,us), args)
  else
    explicitize inctx impl (cf, CAst.make @@ CRef (f,us)) args

let rec fill_arg_scopes args subscopes scopes = match args, subscopes with
| [], _ -> []
| a :: args, scopt :: subscopes ->
  (a, (scopt, scopes)) :: fill_arg_scopes args subscopes scopes
| a :: args, [] ->
  (a, (None, scopes)) :: fill_arg_scopes args [] scopes

let extern_args extern env args =
  let map (arg, argscopes) = lazy (extern argscopes env arg) in
  List.map map args

let match_coercion_app c = match DAst.get c with
  | GApp (r, args) ->
    begin match DAst.get r with
    | GRef (r,_) -> Some (c.CAst.loc, r, 0, args)
    | _ -> None
    end
  | _ -> None

let rec remove_coercions inctx c =
  match match_coercion_app c with
  | Some (loc,r,pars,args) when not (!Flags.raw_print || !print_coercions) ->
      let nargs = List.length args in
      (try match Classops.hide_coercion r with
          | Some n when (n - pars) < nargs && (inctx || (n - pars)+1 < nargs) ->
              (* We skip a coercion *)
              let l = List.skipn (n - pars) args in
              let (a,l) = match l with a::l -> (a,l) | [] -> assert false in
              (* Recursively remove the head coercions *)
              let a' = remove_coercions true a in
              (* Don't flatten App's in case of funclass so that
                 (atomic) notations on [a] work; should be compatible
                 since printer does not care whether App's are
                 collapsed or not and notations with an implicit
                 coercion using funclass either would have already
                 been confused with ordinary application or would have need
                 a surrounding context and the coercion to funclass would
                 have been made explicit to match *)
              if List.is_empty l then a' else DAst.make ?loc @@ GApp (a',l)
          | _ -> c
      with Not_found -> c)
  | _ -> c

let rec flatten_application c = match DAst.get c with
  | GApp (f, l) ->
    begin match DAst.get f with
    | GApp(a,l') ->
      let loc = c.CAst.loc in
      flatten_application (DAst.make ?loc @@ GApp (a,l'@l))
    | _ -> c
    end
  | a -> c

(**********************************************************************)
(* mapping glob_constr to numerals (in presence of coercions, choose the *)
(* one with no delimiter if possible)                                 *)

let extern_possible_prim_token scopes r =
  try
    let (sc,n) = uninterp_prim_token r in
    match availability_of_prim_token n sc scopes with
    | None -> None
    | Some key -> Some (insert_delimiters (CAst.make ?loc:(loc_of_glob_constr r) @@ CPrim n) key)
  with No_match ->
    None

let extern_optimal_prim_token scopes r r' =
  let c = extern_possible_prim_token scopes r in
  let c' = if r==r' then None else extern_possible_prim_token scopes r' in
  match c,c' with
  | Some n, (Some ({ CAst.v = CDelimiters _}) | None) | _, Some n -> n
  | _ -> raise No_match

(**********************************************************************)
(* mapping decl                                                       *)

let extended_glob_local_binder_of_decl loc = function
  | (p,bk,None,t) -> GLocalAssum (p,bk,t)
  | (p,bk,Some x, t) ->
    match DAst.get t with
    | GHole (_, Misctypes.IntroAnonymous, None) -> GLocalDef (p,bk,x,None)
    | _ -> GLocalDef (p,bk,x,Some t)

let extended_glob_local_binder_of_decl ?loc u = DAst.make ?loc (extended_glob_local_binder_of_decl loc u)

(**********************************************************************)
(* mapping glob_constr to constr_expr                                    *)

let extern_glob_sort = function
  | GProp -> GProp
  | GSet -> GSet
  | GType _ as s when !print_universes -> s
  | GType _ -> GType []

let extern_universes = function
  | Some _ as l when !print_universes -> l
  | _ -> None
  
let rec extern inctx scopes vars r =
  let r' = remove_coercions inctx r in
  try
    if !Flags.raw_print || !print_no_symbol then raise No_match;
    extern_optimal_prim_token scopes r r'
  with No_match ->
  try
    let r'' = flatten_application r' in
    if !Flags.raw_print || !print_no_symbol then raise No_match;
    extern_notation scopes vars r'' (uninterp_notations r'')
  with No_match -> lift (fun ?loc -> function
  | GRef (ref,us) ->
      extern_global (select_stronger_impargs (implicits_of_global ref))
        (extern_reference ?loc vars ref) (extern_universes us)

  | GVar id -> CRef (Ident (loc,id),None)

  | GEvar (n,[]) when !print_meta_as_hole -> CHole (None, Misctypes.IntroAnonymous, None)

  | GEvar (n,l) ->
      extern_evar n (List.map (on_snd (extern false scopes vars)) l)

  | GPatVar kind ->
      if !print_meta_as_hole then CHole (None, Misctypes.IntroAnonymous, None) else
       (match kind with
         | Evar_kinds.SecondOrderPatVar n -> CPatVar n
         | Evar_kinds.FirstOrderPatVar n -> CEvar (n,[]))

  | GApp (f,args) ->
      (match DAst.get f with
         | GRef (ref,us) ->
            let rloc = f.CAst.loc in
             let subscopes = find_arguments_scope ref in
             let args = fill_arg_scopes args subscopes (snd scopes) in
             begin
               try
                 if !Flags.raw_print then raise Exit;
                 let cstrsp = match ref with ConstructRef c -> c | _ -> raise Not_found in
                 let struc = Recordops.lookup_structure (fst cstrsp) in
                 if PrintingRecord.active (fst cstrsp) then
                   ()
                 else if PrintingConstructor.active (fst cstrsp) then
                   raise Exit
                 else if not !record_print then
                   raise Exit;
                 let projs = struc.Recordops.s_PROJ in
                 let locals = struc.Recordops.s_PROJKIND in
                 let rec cut args n =
                   if Int.equal n 0 then args
                   else
                     match args with
                     | [] -> raise No_match
                     | _ :: t -> cut t (n - 1) in
                 let args = cut args struc.Recordops.s_EXPECTEDPARAM in
                 let rec ip projs locs args acc =
                   match projs with
                     | [] -> acc
                     | None :: q -> raise No_match
                     | Some c :: q ->
                         match locs with
                           | [] -> anomaly (Pp.str "projections corruption [Constrextern.extern].")
                           | (_, false) :: locs' ->
                               (* we don't want to print locals *)
                               ip q locs' args acc
                           | (_, true) :: locs' ->
                               match args with
                                 | [] -> raise No_match
                                     (* we give up since the constructor is not complete *)
                                 | (arg, scopes) :: tail ->
                                     let head = extern true scopes vars arg in
                                     ip q locs' tail ((extern_reference ?loc Id.Set.empty (ConstRef c), head) :: acc)
                   in
                 CRecord (List.rev (ip projs locals args []))
               with
                 | Not_found | No_match | Exit ->
                    let args = extern_args (extern true) vars args in
                     extern_app inctx
                       (select_stronger_impargs (implicits_of_global ref))
                       (Some ref,extern_reference ?loc:rloc vars ref) (extern_universes us) args
             end

         | _       ->
           explicitize inctx [] (None,sub_extern false scopes vars f)
             (List.map (fun c -> lazy (sub_extern true scopes vars c)) args))

  | GLetIn (na,b,t,c) ->
      CLetIn ((loc,na),sub_extern false scopes vars b,
              Option.map (extern_typ scopes vars) t,
              extern inctx scopes (add_vname vars na) c)

  | GProd (na,bk,t,c) ->
      let t = extern_typ scopes vars t in
      let (idl,c) = factorize_prod scopes (add_vname vars na) na bk t c in
      CProdN ([(Loc.tag na)::idl,Default bk,t],c)

  | GLambda (na,bk,t,c) ->
      let t = extern_typ scopes vars t in
      let (idl,c) = factorize_lambda inctx scopes (add_vname vars na) na bk t c in
      CLambdaN ([(Loc.tag na)::idl,Default bk,t],c)

  | GCases (sty,rtntypopt,tml,eqns) ->
    let vars' =
      List.fold_right (Name.fold_right Id.Set.add)
        (cases_predicate_names tml) vars in
    let rtntypopt' = Option.map (extern_typ scopes vars') rtntypopt in
    let tml = List.map (fun (tm,(na,x)) ->
                 let na' = match na, DAst.get tm with
                   | Anonymous, GVar id ->
                      begin match rtntypopt with
                            | None -> None
                            | Some ntn ->
                               if occur_glob_constr id ntn then
                                 Some (Loc.tag Anonymous)
                               else None
                      end
                   | Anonymous, _ -> None
                   | Name id, GVar id' when Id.equal id id' -> None
                   | Name _, _ -> Some (Loc.tag na) in
                 (sub_extern false scopes vars tm,
                  na',
                  Option.map (fun (loc,(ind,nal)) ->
                              let args = List.map (fun x -> DAst.make @@ PatVar x) nal in
                              let fullargs = add_cpatt_for_params ind args in
                              extern_ind_pattern_in_scope scopes vars ind fullargs
                             ) x))
                tml
    in
    let eqns = List.map (extern_eqn inctx scopes vars) eqns in
    CCases (sty,rtntypopt',tml,eqns)

  | GLetTuple (nal,(na,typopt),tm,b) ->
      CLetTuple (List.map (fun na -> (Loc.tag na)) nal,
        (Option.map (fun _ -> (Loc.tag na)) typopt,
         Option.map (extern_typ scopes (add_vname vars na)) typopt),
        sub_extern false scopes vars tm,
        extern inctx scopes (List.fold_left add_vname vars nal) b)

  | GIf (c,(na,typopt),b1,b2) ->
      CIf (sub_extern false scopes vars c,
        (Option.map (fun _ -> (Loc.tag na)) typopt,
         Option.map (extern_typ scopes (add_vname vars na)) typopt),
        sub_extern inctx scopes vars b1, sub_extern inctx scopes vars b2)

  | GRec (fk,idv,blv,tyv,bv) ->
      let vars' = Array.fold_right Id.Set.add idv vars in
      (match fk with
         | GFix (nv,n) ->
             let listdecl =
               Array.mapi (fun i fi ->
                 let (bl,ty,def) = blv.(i), tyv.(i), bv.(i) in
                 let bl = List.map (extended_glob_local_binder_of_decl ?loc) bl in
                 let (assums,ids,bl) = extern_local_binder scopes vars bl in
                 let vars0 = List.fold_right (Name.fold_right Id.Set.add) ids vars in
                 let vars1 = List.fold_right (Name.fold_right Id.Set.add) ids vars' in
                 let n =
                   match fst nv.(i) with
                     | None -> None
                     | Some x -> Some (Loc.tag @@ Name.get_id (List.nth assums x))
                 in
                 let ro = extern_recursion_order scopes vars (snd nv.(i)) in
                 ((Loc.tag fi), (n, ro), bl, extern_typ scopes vars0 ty,
                  extern false scopes vars1 def)) idv
             in
             CFix ((loc,idv.(n)),Array.to_list listdecl)
         | GCoFix n ->
             let listdecl =
               Array.mapi (fun i fi ->
                 let bl = List.map (extended_glob_local_binder_of_decl ?loc) blv.(i) in
                 let (_,ids,bl) = extern_local_binder scopes vars bl in
                 let vars0 = List.fold_right (Name.fold_right Id.Set.add) ids vars in
                 let vars1 = List.fold_right (Name.fold_right Id.Set.add) ids vars' in
                 ((Loc.tag fi),bl,extern_typ scopes vars0 tyv.(i),
                  sub_extern false scopes vars1 bv.(i))) idv
             in
             CCoFix ((loc,idv.(n)),Array.to_list listdecl))

  | GSort s -> CSort (extern_glob_sort s)

  | GHole (e,naming,_) -> CHole (Some e, naming, None) (** TODO: extern tactics. *)

  | GCast (c, c') ->
      CCast (sub_extern true scopes vars c,
             Miscops.map_cast_type (extern_typ scopes vars) c')
  ) r'

and extern_typ (_,scopes) =
  extern true (Notation.current_type_scope_name (),scopes)

and sub_extern inctx (_,scopes) = extern inctx (None,scopes)

and factorize_prod scopes vars na bk aty c =
  let c = extern_typ scopes vars c in
  match na, c with
  | Name id, { CAst.loc ; v = CProdN ([nal,Default bk',ty],c) }
      when binding_kind_eq bk bk' && constr_expr_eq aty ty
      && not (occur_var_constr_expr id ty) (* avoid na in ty escapes scope *) ->
      nal,c
  | _ ->
      [],c

and factorize_lambda inctx scopes vars na bk aty c =
  let c = sub_extern inctx scopes vars c in
  match c with
  | { CAst.loc; v = CLambdaN ([nal,Default bk',ty],c) }
      when binding_kind_eq bk bk' && constr_expr_eq aty ty
      && not (occur_name na ty) (* avoid na in ty escapes scope *) ->
      nal,c
  | _ ->
      [],c

and extern_local_binder scopes vars = function
    [] -> ([],[],[])
  | b :: l ->
    match DAst.get b with
    | GLocalDef (na,bk,bd,ty) ->
      let (assums,ids,l) =
        extern_local_binder scopes (Name.fold_right Id.Set.add na vars) l in
      (assums,na::ids,
       CLocalDef((Loc.tag na), extern false scopes vars bd,
                   Option.map (extern false scopes vars) ty) :: l)

    | GLocalAssum (na,bk,ty) ->
      let ty = extern_typ scopes vars ty in
      (match extern_local_binder scopes (Name.fold_right Id.Set.add na vars) l with
          (assums,ids,CLocalAssum(nal,k,ty')::l)
            when constr_expr_eq ty ty' &&
              match na with Name id -> not (occur_var_constr_expr id ty')
                | _ -> true ->
              (na::assums,na::ids,
               CLocalAssum((Loc.tag na)::nal,k,ty')::l)
        | (assums,ids,l) ->
            (na::assums,na::ids,
             CLocalAssum([(Loc.tag na)],Default bk,ty) :: l))

    | GLocalPattern ((p,_),_,bk,ty) ->
      let ty =
        if !Flags.raw_print then Some (extern_typ scopes vars ty) else None in
      let p = extern_cases_pattern vars p in
      let (assums,ids,l) = extern_local_binder scopes vars l in
      (assums,ids, CLocalPattern(Loc.tag @@ (p,ty)) :: l)

and extern_eqn inctx scopes vars (loc,(ids,pl,c)) =
  Loc.tag ?loc ([loc,List.map (extern_cases_pattern_in_scope scopes vars) pl],
   extern inctx scopes vars c)

and extern_notation (tmp_scope,scopes as allscopes) vars t = function
  | [] -> raise No_match
  | (keyrule,pat,n as _rule)::rules ->
      let loc = Glob_ops.loc_of_glob_constr t in
      try
        if is_inactive_rule keyrule then raise No_match;
        (* Adjusts to the number of arguments expected by the notation *)
        let (t,args,argsscopes,argsimpls) = match DAst.get t ,n with
          | GApp (f,args), Some n
              when List.length args >= n ->
              let args1, args2 = List.chop n args in
              let subscopes, impls =
                match DAst.get f with
                | GRef (ref,us) ->
                  let subscopes =
                    try List.skipn n (find_arguments_scope ref)
                    with Failure _ -> [] in
                  let impls =
                    let impls =
                      select_impargs_size
                        (List.length args) (implicits_of_global ref) in
                    try List.skipn n impls with Failure _ -> [] in
                  subscopes,impls
                | _ ->
                  [], [] in
              (if Int.equal n 0 then f else DAst.make @@ GApp (f,args1)),
              args2, subscopes, impls
          | GApp (f, args), None ->
            begin match DAst.get f with
            | GRef (ref,us) ->
              let subscopes = find_arguments_scope ref in
              let impls =
                  select_impargs_size
                    (List.length args) (implicits_of_global ref) in
              f, args, subscopes, impls
            | _ -> t, [], [], []
            end
          | GRef (ref,us), Some 0 -> DAst.make @@ GApp (t,[]), [], [], []
          | _, None -> t, [], [], []
          | _ -> raise No_match in
        (* Try matching ... *)
        let terms,termlists,binders =
          match_notation_constr !print_universes t pat in
        (* Try availability of interpretation ... *)
        let e =
          match keyrule with
          | NotationRule (sc,ntn) ->
              (match availability_of_notation (sc,ntn) allscopes with
                  (* Uninterpretation is not allowed in current context *)
              | None -> raise No_match
                  (* Uninterpretation is allowed in current context *)
              | Some (scopt,key) ->
                  let scopes' = Option.List.cons scopt scopes in
                  let l =
                    List.map (fun (c,(scopt,scl)) ->
                      extern (* assuming no overloading: *) true
                        (scopt,scl@scopes') vars c)
                      terms in
                  let ll =
                    List.map (fun (c,(scopt,scl)) ->
                      List.map (extern true (scopt,scl@scopes') vars) c)
                      termlists in
                  let bll =
                    List.map (fun (bl,(scopt,scl)) ->
                      pi3 (extern_local_binder (scopt,scl@scopes') vars bl))
                      binders in
                  insert_delimiters (make_notation loc ntn (l,ll,bll)) key)
          | SynDefRule kn ->
              let l =
                List.map (fun (c,(scopt,scl)) ->
                  extern true (scopt,scl@scopes) vars c, None)
                  terms in
              let a = CRef (Qualid (loc, shortest_qualid_of_syndef vars kn),None) in
              CAst.make ?loc @@ if List.is_empty l then a else CApp ((None, CAst.make a),l) in
         if List.is_empty args then e
        else
          let args = fill_arg_scopes args argsscopes scopes in
          let args = extern_args (extern true) vars args in
          CAst.make ?loc @@ explicitize false argsimpls (None,e) args
      with
          No_match -> extern_notation allscopes vars t rules

and extern_recursion_order scopes vars = function
    GStructRec -> CStructRec
  | GWfRec c -> CWfRec (extern true scopes vars c)
  | GMeasureRec (m,r) -> CMeasureRec (extern true scopes vars m,
                                     Option.map (extern true scopes vars) r)


let extern_glob_constr vars c =
  extern false (None,[]) vars c

let extern_glob_type vars c =
  extern_typ (None,[]) vars c

(******************************************************************)
(* Main translation function from constr -> constr_expr *)

let extern_constr_gen lax goal_concl_style scopt env sigma t =
  (* "goal_concl_style" means do alpha-conversion using the "goal" convention *)
  (* i.e.: avoid using the names of goal/section/rel variables and the short *)
  (* names of global definitions of current module when computing names for *)
  (* bound variables. *)
  (* Not "goal_concl_style" means do alpha-conversion avoiding only *)
  (* those goal/section/rel variables that occurs in the subterm under *)
  (* consideration; see namegen.ml for further details *)
  let avoid = if goal_concl_style then vars_of_env env else Id.Set.empty in
  let r = Detyping.detype Detyping.Later ~lax:lax goal_concl_style avoid env sigma t in
  let vars = vars_of_env env in
  extern false (scopt,[]) vars r

let extern_constr_in_scope goal_concl_style scope env sigma t =
  extern_constr_gen false goal_concl_style (Some scope) env sigma t

let extern_constr ?(lax=false) goal_concl_style env sigma t =
  extern_constr_gen lax goal_concl_style None env sigma t

let extern_type goal_concl_style env sigma t =
  let avoid = if goal_concl_style then vars_of_env env else Id.Set.empty in
  let r = Detyping.detype Detyping.Later goal_concl_style avoid env sigma t in
  extern_glob_type (vars_of_env env) r

let extern_sort sigma s = extern_glob_sort (detype_sort sigma s)

let extern_closed_glob ?lax goal_concl_style env sigma t =
  let avoid = if goal_concl_style then vars_of_env env else Id.Set.empty in
  let r =
    Detyping.detype_closed_glob ?lax goal_concl_style avoid env sigma t
  in
  let vars = vars_of_env env in
  extern false (None,[]) vars r

(******************************************************************)
(* Main translation function from pattern -> constr_expr *)

let any_any_branch =
  (* | _ => _ *)
  Loc.tag ([],[DAst.make @@ PatVar Anonymous], DAst.make @@ GHole (Evar_kinds.InternalHole,Misctypes.IntroAnonymous,None))

let compute_displayed_name_in_pattern sigma avoid na c =
  let open Namegen in
  compute_displayed_name_in_gen (fun _ -> Patternops.noccurn_pattern) sigma avoid na c

let rec glob_of_pat avoid env sigma pat = DAst.make @@ match pat with
  | PRef ref -> GRef (ref,None)
  | PVar id  -> GVar id
  | PEvar (evk,l) ->
      let test decl = function PVar id' -> Id.equal (NamedDecl.get_id decl) id' | _ -> false in
      let l = Evd.evar_instance_array test (Evd.find sigma evk) l in
      let id = match Evd.evar_ident evk sigma with
      | None -> Id.of_string "__"
      | Some id -> id
      in
      GEvar (id,List.map (on_snd (glob_of_pat avoid env sigma)) l)
  | PRel n ->
      let id = try match lookup_name_of_rel n env with
        | Name id   -> id
        | Anonymous ->
            anomaly ~label:"glob_constr_of_pattern" (Pp.str "index to an anonymous variable.")
      with Not_found -> Id.of_string ("_UNBOUND_REL_"^(string_of_int n)) in
      GVar id
  | PMeta None -> GHole (Evar_kinds.InternalHole, Misctypes.IntroAnonymous,None)
  | PMeta (Some n) -> GPatVar (Evar_kinds.FirstOrderPatVar n)
  | PProj (p,c) -> GApp (DAst.make @@ GRef (ConstRef (Projection.constant p),None),
                         [glob_of_pat avoid env sigma c])
  | PApp (f,args) ->
      GApp (glob_of_pat avoid env sigma f,Array.map_to_list (glob_of_pat avoid env sigma) args)
  | PSoApp (n,args) ->
      GApp (DAst.make @@ GPatVar (Evar_kinds.SecondOrderPatVar n),
        List.map (glob_of_pat avoid env sigma) args)
  | PProd (na,t,c) ->
      let na',avoid' = compute_displayed_name_in_pattern sigma avoid na c in
      let env' = Termops.add_name na' env in
      GProd (na',Explicit,glob_of_pat avoid env sigma t,glob_of_pat avoid' env' sigma c)
  | PLetIn (na,b,t,c) ->
      let na',avoid' = Namegen.compute_displayed_let_name_in sigma Namegen.RenamingForGoal avoid na c in
      let env' = Termops.add_name na' env in
      GLetIn (na',glob_of_pat avoid env sigma b, Option.map (glob_of_pat avoid env sigma) t,
              glob_of_pat avoid' env' sigma c)
  | PLambda (na,t,c) ->
      let na',avoid' = compute_displayed_name_in_pattern sigma avoid na c in
      let env' = Termops.add_name na' env in
      GLambda (na',Explicit,glob_of_pat avoid env sigma t, glob_of_pat avoid' env' sigma c)
  | PIf (c,b1,b2) ->
      GIf (glob_of_pat avoid env sigma c, (Anonymous,None),
           glob_of_pat avoid env sigma b1, glob_of_pat avoid env sigma b2)
  | PCase ({cip_style=LetStyle; cip_ind_tags=None},PMeta None,tm,[(0,n,b)]) ->
      let nal,b = it_destRLambda_or_LetIn_names n (glob_of_pat avoid env sigma b) in
      GLetTuple (nal,(Anonymous,None),glob_of_pat avoid env sigma tm,b)
  | PCase (info,p,tm,bl) ->
      let mat = match bl, info.cip_ind with
        | [], _ -> []
        | _, Some ind ->
          let bl' = List.map (fun (i,n,c) -> (i,n,glob_of_pat avoid env sigma c)) bl in
          simple_cases_matrix_of_branches ind bl'
        | _, None -> anomaly (Pp.str "PCase with some branches but unknown inductive.")
      in
      let mat = if info.cip_extensible then mat @ [any_any_branch] else mat
      in
      let indnames,rtn = match p, info.cip_ind, info.cip_ind_tags with
        | PMeta None, _, _ -> (Anonymous,None),None
        | _, Some ind, Some nargs ->
          return_type_of_predicate ind nargs (glob_of_pat avoid env sigma p)
        | _ -> anomaly (Pp.str "PCase with non-trivial predicate but unknown inductive.")
      in
      GCases (RegularStyle,rtn,[glob_of_pat avoid env sigma tm,indnames],mat)
  | PFix f -> DAst.get (Detyping.detype_names false avoid env (Global.env()) sigma (EConstr.of_constr (mkFix f))) (** FIXME bad env *)
  | PCoFix c -> DAst.get (Detyping.detype_names false avoid env (Global.env()) sigma (EConstr.of_constr (mkCoFix c)))
  | PSort s -> GSort s

let extern_constr_pattern env sigma pat =
  extern true (None,[]) Id.Set.empty (glob_of_pat Id.Set.empty env sigma pat)

let extern_rel_context where env sigma sign =
  let a = detype_rel_context Detyping.Later where Id.Set.empty (names_of_rel_context env,env) sigma sign in
  let vars = vars_of_env env in
  let a = List.map (extended_glob_local_binder_of_decl) a in
  pi3 (extern_local_binder (None,[]) vars a)
interp/constrextern.ml

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